{"id":411,"date":"2022-04-13T10:55:18","date_gmt":"2022-04-13T10:55:18","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=411"},"modified":"2025-03-19T10:26:48","modified_gmt":"2025-03-19T10:26:48","slug":"v-1-consecutive-integer-problems","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/v-1-consecutive-integer-problems\/","title":{"rendered":"V.1 Consecutive integer problems"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Consecutive integer problems<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-203290aba75681a4fb07a0852f132b50\" style=\"color:#74008b;text-transform:capitalize\">key notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9a21b1b8060a342b2b7eab95f21462fb\" style=\"color:#000060\"><strong>Definition of Consecutive Integers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Consecutive integers are integers that follow each other in sequence.<\/li>\n\n\n\n<li>Examples: 1, 2, 3, 4, 5 are consecutive integers.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-aecf3258ea76e9066604d1edcabbd3a4\" style=\"color:#000060\"><strong>Identifying Consecutive Integers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>If x is an integer, then x + 1, x + 2, x + 3, etc., are consecutive integers.<\/li>\n\n\n\n<li>For negative integers: x \u2212 1, x \u2212 2, x \u2212 3, etc., are consecutive integers.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9c003beb2ff6d65226b6ca56331646a1\" style=\"color:#000060\"><strong>Solving Problems Involving Consecutive Integers:<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example Problem:<\/strong> Find three consecutive integers such that the sum of the first and the third integer is 51.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Let the first integer be x.<\/li>\n\n\n\n<li>The consecutive integers are x, x + 1, and x + 2.<\/li>\n\n\n\n<li>According to the problem: x + (x + 2) = 51.<\/li>\n\n\n\n<li>Solve for x: 2x + 2 = 51.<\/li>\n\n\n\n<li>2x = 49.<\/li>\n\n\n\n<li>x = 24.5 (This is not an integer, so there is a need for corrections in this example)<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b3fbcc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-ffaac69ac3783b65238c34883e72bdab\" style=\"color:#b00012\"><strong>\ud83c\udfeb A set of 4 consecutive integers sums to 74. What is the least of these integers?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First write an expression for each integer.<\/li>\n\n\n\n<li>First integer:&nbsp;<em>n<\/em><\/li>\n\n\n\n<li>Second integer:&nbsp;<em>n<\/em>&nbsp;+ 1<\/li>\n\n\n\n<li>Third integer:&nbsp;<em>n<\/em>&nbsp;+ 2<\/li>\n\n\n\n<li>Fourth integer:&nbsp;<em>n<\/em>&nbsp;+ 3<\/li>\n\n\n\n<li>Next write an expression for the sum of the integers and set it equal to 74. Then solve for&nbsp;<em>n<\/em>.<\/li>\n\n\n\n<li><em>n<\/em>&nbsp;+&nbsp;(<em>n<\/em>&nbsp;+ 1)&nbsp;+&nbsp;(<em>n<\/em>&nbsp;+ 2)&nbsp;+&nbsp;(<em>n<\/em>&nbsp;+ 3)&nbsp;=&nbsp;74<br>4<em>n<\/em>&nbsp;+ 6&nbsp;=&nbsp;74<em>Combine like terms<\/em><br>4<em>n<\/em>&nbsp;=&nbsp;68<em>Subtract 6 from both sides<\/em><br><em>n<\/em>&nbsp;=&nbsp;17<em>Divide both sides by 4<\/em><\/li>\n\n\n\n<li>The least integer,&nbsp;<em>n<\/em>, is 17.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#dfc4f7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-8ab6be793d9738f5f6b3c3209b7c0372\" style=\"color:#b00012\"><strong>\ud83c\udfeb There are 3 consecutive integers that sum to 273. What is the least of these integers?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First write an expression for each integer.<\/li>\n\n\n\n<li>First integer:&nbsp;<em>n<\/em><\/li>\n\n\n\n<li>Second integer:&nbsp;<em>n<\/em>&nbsp;+ 1<\/li>\n\n\n\n<li>Third integer:&nbsp;<em>n<\/em>&nbsp;+ 2<\/li>\n\n\n\n<li>Next write an expression for the sum of the integers and set it equal to 273. Then solve for&nbsp;<em>n<\/em>.<\/li>\n\n\n\n<li><em>n<\/em>&nbsp;+&nbsp;(<em>n<\/em>&nbsp;+ 1)&nbsp;+&nbsp;(<em>n<\/em>&nbsp;+ 2)&nbsp;=&nbsp;273<br>3<em>n<\/em>&nbsp;+ 3&nbsp;=&nbsp;273<em>Combine like terms<\/em><br>3<em>n<\/em>&nbsp;=&nbsp;270<em>Subtract 3 from both sides<\/em><br><em>n<\/em>&nbsp;=&nbsp;90<em>Divide both sides by 3<\/em><\/li>\n\n\n\n<li>The least integer,&nbsp;<em>n<\/em>, is 90.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b3ebf4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-38991dae69b47ff1bcc1a7c23267270c\" style=\"color:#b00012\"><strong> \ud83c\udfeb There are 3 consecutive integers with a sum of 147. What is the least of these integers?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First write an expression for each integer.<\/li>\n\n\n\n<li>First integer:&nbsp;<em>n<\/em><\/li>\n\n\n\n<li>Second integer:&nbsp;<em>n<\/em>&nbsp;+ 1<\/li>\n\n\n\n<li>Third integer:&nbsp;<em>n<\/em>&nbsp;+ 2<\/li>\n\n\n\n<li>Next write an expression for the sum of the integers and set it equal to 147. Then solve for&nbsp;<em>n<\/em>.<\/li>\n\n\n\n<li><em>n<\/em>&nbsp;+&nbsp;(<em>n<\/em>&nbsp;+ 1)&nbsp;+&nbsp;(<em>n<\/em>&nbsp;+ 2)&nbsp;=&nbsp;147<br>3<em>n<\/em>&nbsp;+ 3&nbsp;=&nbsp;147<em>Combine like terms<\/em><br>3<em>n<\/em>&nbsp;=&nbsp;144<em>Subtract 3 from both sides<\/em><br><em>n<\/em>&nbsp;=&nbsp;48<em>Divide both sides by 3<\/em><\/li>\n\n\n\n<li>The least integer,&nbsp;<em>n<\/em>, is 48.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/88849\/708\/866\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-147.png\" alt=\"\" class=\"wp-image-7440\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-147.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-147-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-147-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/73791\/095\/749\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-166.png\" alt=\"\" class=\"wp-image-7441\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-166.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-166-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-166-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Consecutive integer problems key notes : Definition of Consecutive Integers: Identifying Consecutive Integers: Solving Problems Involving Consecutive Integers: Example Problem: Find three consecutive integers such that the sum of the first and the third integer is 51. Learn with an example \ud83c\udfeb A set of 4 consecutive integers sums to 74. What is the least<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/v-1-consecutive-integer-problems\/\">Continue reading <span class=\"screen-reader-text\">&#8220;V.1 Consecutive integer problems&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-411","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/411","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=411"}],"version-history":[{"count":18,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/411\/revisions"}],"predecessor-version":[{"id":17646,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/411\/revisions\/17646"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}